Finite Group Databasebeta

← #14283131

Subgroups — #14283131

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4076C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic, complemented
3C4×C5×#217C211yesmaximal, characteristic, complemented
4#11745954C214yesmaximal, complemented
5#10600237—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C3×C22⋊D5—21no—
8C22×C3×D20C411yescharacteristic, complemented
9C2×#6710—21no—
10C2×C5×#217—21no—
11C2×C4×C5×Dic3—21no—
12C3×#4076—21no—
13C3×#4076—21no—
14C3×#4076C412yescomplemented
15C3×#4076C2212yes—
16C2×C3×#685—21no—
17C2×C3×C4⋊Dic5C411yescharacteristic, complemented
18#91114—21no—
19#91114C2212yescomplemented
20C5×C3⋊#95C2212yescomplemented
21#71673—51nomaximal, Hall
22C2×#4076D311yescharacteristic
23C4×C5×C22⋊C4—31no—
24#65496—31no—
25#64671—34no—
26C24×C3×C5D411yescharacteristic
27C23×C3×D5—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—22no—
38C2×C3×C22⋊D5—44no—
39C22×C3×Dic5—21no—
40C2×C3×D20—21no—
41C2×C3×D20—42no—
42C2×C3×D20C2×C412yes—
43#6710—42no—
44C2×C3⋊#168—22no—
45C5×#217—24no—
46C4×C5×Dic3—42no—
47C3×#685—22no—
48C3×#685—22no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5C2×C412yes—
51C2×C3×#121—51no—
52C4×#217D511yescharacteristic, complemented
53#5207—51no—
54#4537—54no—
55C23×C4×C5C2×D311yescharacteristic
56C22×C22⋊D5—21no—
57C22×D20Dic311yescharacteristic, complemented
58C2×C5×C22⋊C4—61no—
59C2×C42×C5—61no—
60#4076—21no—
61#4076—21no—
62#4076Dic312yescomplemented
63#4076C2×D312yes—
64C2×#685—21no—
65C2×C4⋊Dic5Dic311yescharacteristic, complemented
66C2×#681—61no—
67C5×#95—32no—
68C22⋊#168—32no—
69C22⋊#168—61no—
70#1507—151noSylow
71C23×C3×C5—22no—
72C23×C3×C5—22no—
73C23×C3×C5—41no—
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C22⋊C411yescharacteristic
76C23×C3×C5C2×D411yescharacteristic
77C22×C3×D5—22no—
78C22×C3×D5—42no—
79C22×C3×D5—42no—
80C22×C3×D5—42no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5—41no—
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22⋊C411yescharacteristic
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C5×Dic3—24no—
92C2×C5×Dic3—42no—
93C2×C5×Dic3—42no—
94C3×C22⋊D5—44no—
95C3×C22⋊D5—44no—
96C2×C3×Dic5—22no—
97C2×C3×Dic5—42no—
98C3×D20—42no—
99C3×D20—42no—
100C3⋊#168—42no—
101C22×C3×D4—51no—
102C22×C3×D4—101no—
103C23×C3×C4C2×D511yescharacteristic
104C3×#121—52no—
105C3×#121—52no—
106C3×#121—101no—
107C3×#121—101no—
108C2×C3×C4⋊C4—51no—
109C2×C3×C22⋊C4—101no—
110C2×#217—21no—
111C2×C4×Dic3—21no—
112C2×#208—101no—
113C3⋊#95C2×D512yescomplemented
114#830—52no—
115#830—101no—
116C24×C5#6711yescharacteristic
117C23×D5—21no—
118C22×C4×C5—42no—
119C22×C4×C5—62no—
120C22×C4×C5C2×Dic311yescharacteristic
121C22×C4×C5C2×Dic311yescharacteristic
122C22×C4×C5#6711yescharacteristic
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5#6711yescharacteristic
125C22×C4×C5C22×D311yescharacteristic
126C2×C22⋊D5—22no—
127C2×C22⋊D5—22no—
128C2×C22⋊D5—44no—
129C22×Dic5—21no—
130C2×D20—21no—
131C2×D20—42no—
132C2×D20C2×Dic312yes—
133C5×C22⋊C4—64no—
134C42×C5—122no—
135#685—22no—
136#685—22no—
137C4⋊Dic5—21no—
138C4⋊Dic5C2×Dic312yes—
139#681—122no—
140C2×#168—62no—
141C2×#121—51no—
142#407—151no—
143C4×C22⋊C4—31no—
144#327—154no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—44no—
153C22×C3×C5#10412yes—
154C22×C3×C5C2×C22⋊C411yescharacteristic
155C22×C3×C5AGL(1,ℤ/8)12yes—
156C2×C3×D5—42no—
157C2×C3×D5—42no—
158C2×C3×D5—42no—
159C2×C3×D5—84no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5#9912yes—
164C3×Dic5—42no—
165C5×Dic3—44no—
166C24×C3—101no—
167C24×C3C22⋊D511yescharacteristic
168C2×C3×D4—52no—
169C2×C3×D4—102no—
170C2×C3×D4—102no—
171C2×C3×D4—101no—
172C2×C3×D4—202no—
173C2×C3×D4—204no—
174C22×C3×C4—42no—
175C22×C3×C4—101no—
176C22×C3×C4C4×D511yescharacteristic
177C22×C3×C4C4×D511yescharacteristic
178C22×C3×C4D2011yescharacteristic
179C22×C3×C4D2011yescharacteristic
180C22×C3×C4C22⋊D511yescharacteristic
181C22×C3×C4C22×D511yescharacteristic
182C22×Dic3—22no—
183C3×C4⋊C4—52no—
184C3×C4⋊C4—101no—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—102no—
187#217—24no—
188C4×Dic3—42no—
189#208—202no—
190C2×C3⋊C8—102no—
191C23×C5—22no—
192C23×C5—22no—
193C23×C5—41no—
194C23×C5#21711yescharacteristic
195C23×C5#21711yescharacteristic
196C23×C5C2×#6711yescharacteristic
197C22×D5—22no—
198C22×D5—42no—
199C22×D5—42no—
200C22×D5—42no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—64no—
208C2×C4×C5—122no—
209C2×C4×C5—122no—
210C2×C4×C5#21711yescharacteristic
211C2×C4×C5#21711yescharacteristic
212C2×C4×C5C22×Dic311yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C22⋊D5—44no—
215C22⋊D5—44no—
216C2×Dic5—22no—
217C2×Dic5—42no—
218D20—42no—
219D20—42no—
220#168—122no—
221C22×D4—51no—
222C22×D4—101no—
223C23×C4D3×D511yescharacteristic
224C2×M16—301no—
225#121—52no—
226#121—52no—
227#121—101no—
228#121—101no—
229C2×C4⋊C4—51no—
230C2×C22⋊C4—61no—
231C2×C22⋊C4—101no—
232C2×C42—61no—
233C22⋊C8—152no—
234C22⋊C8—301no—
235#95—32no—
236C2×C3×C5—22no—
237C2×C3×C5—22no—
238C2×C3×C5—41no—
239C2×C3×C5C2×#9911yescharacteristic
240C2×C3×C5#41811yescharacteristic
241C2×C3×C5C2×#10411yescharacteristic
242C3×D5—82no—
243C23×C3—22no—
244C23×C3—22no—
245C23×C3—41no—
246C23×C3—102no—
247C23×C3—202no—
248C23×C3—202no—
249C23×C3—202no—
250C23×C3#68511yescharacteristic
251C23×C3#68511yescharacteristic
252C23×C3C2×C22⋊D511yescharacteristic
253C3×D4—202no—
254C3×D4—204no—
255C3×D4—204no—
256C3×D4—202no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—102no—
264C2×C3×C4—202no—
265C2×C3×C4#68511yescharacteristic
266C2×C3×C4#68511yescharacteristic
267C2×C3×C4C2×C4×D511yescharacteristic
268C2×C3×C4C2×D2011yescharacteristic
269C2×Dic3—24no—
270C2×Dic3—42no—
271C2×Dic3—42no—
272C3⋊C8—202no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5—44no—
281C22×C5#83712yes—
282C22×C5#93212yes—
283C22×C5C2×#21711yescharacteristic
284C2×D5—42no—
285C2×D5—42no—
286C2×D5—42no—
287C2×D5—84no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—124no—
292C4×C5#83412yes—
293Dic5—42no—
294C24—101no—
295C24#120111yescharacteristic
296C2×D4—52no—
297C2×D4—102no—
298C2×D4—102no—
299C2×D4—101no—
300C2×D4—202no—
301C2×D4—204no—
302C22×C4—42no—
303C22×C4—62no—
304C22×C4—101no—
305C22×C4D5×Dic311yescharacteristic
306C22×C4D5×Dic311yescharacteristic
307C22×C4#120111yescharacteristic
308C22×C4#120211yescharacteristic
309C22×C4#120211yescharacteristic
310C22×C4C2×D3×D511yescharacteristic
311M16—602no—
312C2×C8—302no—
313C4⋊C4—52no—
314C4⋊C4—101no—
315C22⋊C4—64no—
316C22⋊C4—102no—
317C22⋊C4—102no—
318C42—122no—
319C3×C5#150711yescharacteristic, complemented, Hall
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—44no—
328C22×C3—202no—
329C22×C3—202no—
330C22×C3—202no—
331C22×C3—404no—
332C22×C3#393712yes—
333C22×C3C2×#68511yescharacteristic
334C22×C3#409512yes—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—202no—
339C3×C4#393812yes—
340Dic3—44no—
341C2×C5—22no—
342C2×C5—22no—
343C2×C5—41no—
344C2×C5#521511yescharacteristic
345C2×C5C2×#83411yescharacteristic
346C2×C5C2×#83711yescharacteristic
347D5—82no—
348C23—22no—
349C23—22no—
350C23—41no—
351C23—102no—
352C23—202no—
353C23—202no—
354C23—202no—
355C23#666511yescharacteristic
356C23#666511yescharacteristic
357C23C2×#120111yescharacteristic
358D4—202no—
359D4—204no—
360D4—204no—
361D4—202no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—64no—
369C2×C4—102no—
370C2×C4—122no—
371C2×C4—122no—
372C2×C4—202no—
373C2×C4#666511yescharacteristic
374C2×C4#666511yescharacteristic
375C2×C4C2×D5×Dic311yescharacteristic
376C2×C4C2×#120211yescharacteristic
377C8—602no—
378C2×C3—22no—
379C2×C3—22no—
380C2×C3—41no—
381C2×C3—402no—
382C2×C3C2×#393711yescharacteristic
383C2×C3C2×#393811yescharacteristic
384C2×C3#6529011yescharacteristic
385C5#7167311yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—202no—
395C22—202no—
396C22—202no—
397C22—404no—
398C22#9097712yes—
399C22#9129812yes—
400C22C2×#666511yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—124no—
405C4—202no—
406C4#9099512yes—
407C3#1060023711yescharacteristic, complemented, Sylow
408C2—22no—
409C2—22no—
410C2—41no—
411C2—402no—
412C2#1174836611yescharacteristic
413C2C2×#9097711yescharacteristic
414C2C2×#9099511yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×#4076C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1507
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11751308C2semidirect
3. C4×C5×#217C2semidirect
4. #11745954C2semidirect
8. C22×C3×D20C4semidirect
14. C3×#4076C4semidirect
17. C2×C3×C4⋊Dic5C4semidirect
19. #91114C22semidirect
20. C5×C3⋊#95C22semidirect
52. C4×#217D5semidirect
57. C22×D20Dic3semidirect
62. #4076Dic3semidirect
65. C2×C4⋊Dic5Dic3semidirect
113. C3⋊#95C2×D5semidirect
319. C3×C5#1507semidirect
385. C5#71673semidirect
407. C3#10600237semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#40762
#117513082
C4×C5×#2172
#117459542
#106002373
#716735